Hi there
I wanted to offer my experience as I rocked/danced my DS. I did try shush/pat when he was very little but also walked and rocked when he was having difficulty, as he got a little older patting seemed to aggravate his silent reflux so I switched to shush/rub (rubbing his back whilst holding upright as part of wind down) and actually I was swaying my body too so he was still being rocked that way a bit but also the rubbing makes a sort of rocking motion. The way it worked for me was to begin the wind down in you usual way, rocking if that's what you do, then as LO gets more drowsy, reduce the rocking so it becomes reduced to let LO get used to a smaller movement, a very small movement. When you put down (initially it can be when LO is asleep, when that is working put down drowsy) continue the movement by placing a firm hand on the swaddle (near the nappy area, not heavy on the tummy, just firm) and instead of patting move your hand just a little like rubbing to create a rocking motion in the cot. This rocking motion inside the cot with your hand can be reduced in the same way that a pat is reduced. Initially you would use the firm hand with a little rocking motion all the way to sleep and into deep sleep, later you would reduce the amount of rocking, reduce the pressure, do a bit of stop start so that LO knows you are still there and you can increase the rock if needed for little while but always with reduction in mind. Gradually you aim to reduce and stop the rocking just before LO is asleep. Then the next step to rock to drowsy then stop. Next step a little rocking in arms as wind down, into cot awake, maybe a brief rock/rub in the cot whilst you say good night then you leave the room when LO is still awake but happily goes to sleep alone.
If you can get the start of the nap and night sleep improved in this way you may well see the sleep cycle transition improve without specific help. If not then remember at the transition to try to rock in the cot. You can also try a W2S where you begin the rocking before the end of the sleep cycle and rock her through the transition.
Mine actually wasn't swaddled beyond 10 wks but I used to do this firm hand slight rocking in the cot putting my hand on his nappy/hip/tummy when he needed it.
If LO needs picking up of course you can do that. PU and hold even with rocking until calm and drowsy then return to the cot and continue with the firm hand. You can expect at least some of the naps to be messed up and LO to lose a bit of sleep but the long term benefit is huge for LO and you and well worth it in my opinion.
hope this helps
